Turbotax Online uses a subscription model. If you use the free version, your file is locked after October 15 of the year you file. If you use a paid version, you file is locked until October 15 of the year after you file. So your 2014 Deluxe return, filed in 2015, was locked on October 15, 2016. You always have the opportunity to download and print copies for your records before the file is locked, and everyone should do that.
If you have been using paid versions but your old files are locked, you may have used a different account in different years. The system only works if you use the same account every year. It seems to be very common that customers create extra accounts and use them by mistake instead of their original account, and the feedback we get from customer support is that almost every time someone calls in, the answer is they were in the wrong account. Sometimes people create second accounts by mistake. You can use the account recovery tool to see if you might have a second account associated with one of your email addresses. https://myturbotax.intuit.com/account-recovery/
If you are logged into your only account, and you can see all your past returns but they are locked, then you either filed for free in 2016 (even if you paid in the past, you have to pay every year to keep the old returns unlocked) or there is some system error that does not recognize your payment.
For telephone and other support options, see the instructions below.